Unusual light spectra from a two-level atom in squeezed vacuum

We investigate the interaction of an atom with a multi-channel squeezed vacuum. It turns out that the light coming out in a particular channel can have anomalous spectral properties, among them asymmetry of the spectrum, absence of the central peak as well as central hole burning for particular parameters. As an example plane-wave squeezing is considered. In this case the above phenomena can occur for the light spectra in certain directions. In the total spectrum these phenomena are washed out.Comment: 16 pages, LaTeX, 3 figures (included via epsf

Dynamical thermalization and vortex formation in stirred 2D Bose-Einstein condensates

We present a quantum mechanical treatment of the mechanical stirring of Bose-Einstein condensates using classical field techniques. In our approach the condensate and excited modes are described using a Hamiltonian classical field method in which the atom number and (rotating frame) energy are strictly conserved. We simulate a T = 0 quasi-2D condensate perturbed by a rotating anisotropic trapping potential. Vacuum fluctuations in the initial state provide an irreducible mechanism for breaking the initial symmetries of the condensate and seeding the subsequent dynamical instability. Highly turbulent motion develops and we quantify the emergence of a rotating thermal component that provides the dissipation necessary for the nucleation and motional-damping of vortices in the condensate. Vortex lattice formation is not observed, rather the vortices assemble into a spatially disordered vortex liquid state. We discuss methods we have developed to identify the condensate in the presence of an irregular distribution of vortices, determine the thermodynamic parameters of the thermal component, and extract damping rates from the classical field trajectories.Comment: 22 pages, 15 figures. v2: Minor refinements made at suggestion of referee. Discussion of other treatments revised. To appear in Phys. Rev.

Driving the atom by atomic fluorescence: analytic results for the power and noise spectra

We study how the spectral properties of resonance fluorescence propagate through a two-atom system. Within the weak-driving-field approximation we find that, as we go from one atom to the next, the power spectrum exhibits both sub-natural linewidth narrowing and large asymmetries while the spectrum of squeezing narrows but remains otherwise unchanged. Analytical results for the observed spectral features of the fluorescence are provided and their origin is thoroughly discussed.Comment: 13 pages, 5 figures; to be published in Phys. Rev. A Changed title and conten

On separable Fokker-Planck equations with a constant diagonal diffusion matrix

We classify (1+3)-dimensional Fokker-Planck equations with a constant diagonal diffusion matrix that are solvable by the method of separation of variables. As a result, we get possible forms of the drift coefficients $B_1(\vec x),B_2(\vec x),B_3(\vec x)$ providing separability of the corresponding Fokker-Planck equations and carry out variable separation in the latter. It is established, in particular, that the necessary condition for the Fokker-Planck equation to be separable is that the drift coefficients $\vec B(\vec x)$ must be linear. We also find the necessary condition for R-separability of the Fokker-Planck equation. Furthermore, exact solutions of the Fokker-Planck equation with separated variables are constructedComment: 20 pages, LaTe

In-loop squeezing is real squeezing to an in-loop atom

Electro-optical feedback can produce an in-loop photocurrent with arbitrarily low noise. This is not regarded as evidence of `real' squeezing because squeezed light cannot be extracted from the loop using a linear beam splitter. Here I show that illuminating an atom (which is a nonlinear optical element) with `in-loop' squeezed light causes line-narrowing of one quadrature of the atom's fluorescence. This has long been regarded as an effect which can only be produced by squeezing. Experiments on atoms using in-loop squeezing should be much easier than those with conventional sources of squeezed light.Comment: 4 pages, 2 figures, submitted to PR

Thermophoresis of Brownian particles driven by coloured noise

The Brownian motion of microscopic particles is driven by the collisions with the molecules of the surrounding fluid. The noise associated with these collisions is not white, but coloured due, e.g., to the presence of hydrodynamic memory. The noise characteristic time scale is typically of the same order as the time over which the particle's kinetic energy is lost due to friction (inertial time scale). We demonstrate theoretically that, in the presence of a temperature gradient, the interplay between these two characteristic time scales can have measurable consequences on the particle long-time behaviour. Using homogenization theory, we analyse the infinitesimal generator of the stochastic differential equation describing the system in the limit where the two characteristic times are taken to zero; from this generator, we derive the thermophoretic transport coefficient, which, we find, can vary in both magnitude and sign, as observed in experiments. Furthermore, studying the long-term stationary particle distribution, we show that particles can accumulate towards the colder (positive thermophoresis) or the warmer (negative thermophoresis) regions depending on the dependence of their physical parameters and, in particular, their mobility on the temperature.Comment: 9 pages, 4 figure

Response of a two-level atom to a narrow-bandwidth squeezed-vacuum excitation

Using the coupled-system approach we calculate the optical spectra of the fluorescence and transmitted fields of a two-level atom driven by a squeezed vacuum of bandwidths smaller than the natural atomic linewidth. We find that in this regime of squeezing bandwidths the spectra exhibit unique features, such as a hole burning and a three-peak structure, which do not appear for a broadband excitation. We show that the features are unique to the quantum nature of the driving squeezed vacuum field and donor appear when the atom is driven by a classically squeezed field. We find that a quantum squeezed-vacuum field produces squeezing in the emitted fluorescence field which appears only in the squeezing spectrum while there is no squeezing in the total field. We also discuss a nonresonant excitation and find that depending on the squeezing bandwidth there is a peak or a hole in the spectrum at a frequency corresponding to a three-wave-mixing process. The hole appears only for a broadband excitation and results from the strong correlations between squeezed-vacuum photons

Quantum dynamics of impurities in a 1D Bose gas

Using a species-selective dipole potential, we create initially localized impurities and investigate their interactions with a majority species of bosonic atoms in a one-dimensional configuration during expansion. We find an interaction-dependent amplitude reduction of the oscillation of the impurities' size with no measurable frequency shift, and study it as a function of the interaction strength. We discuss possible theoretical interpretations of the data. We compare, in particular, with a polaronic mass shift model derived following Feynman variational approach.Comment: 7 pages, 6 figure

Theory of quantum fluctuations of optical dissipative structures and its application to the squeezing properties of bright cavity solitons

We present a method for the study of quantum fluctuations of dissipative structures forming in nonlinear optical cavities, which we illustrate in the case of a degenerate, type I optical parametric oscillator. The method consists in (i) taking into account explicitly, through a collective variable description, the drift of the dissipative structure caused by the quantum noise, and (ii) expanding the remaining -internal- fluctuations in the biorthonormal basis associated to the linear operator governing the evolution of fluctuations in the linearized Langevin equations. We obtain general expressions for the squeezing and intensity fluctuations spectra. Then we theoretically study the squeezing properties of a special dissipative structure, namely, the bright cavity soliton. After reviewing our previous result that in the linear approximation there is a perfectly squeezed mode irrespectively of the values of the system parameters, we consider squeezing at the bifurcation points, and the squeezing detection with a plane--wave local oscillator field, taking also into account the effect of the detector size on the level of detectable squeezing.Comment: 10 figure

The Escape Problem in a Classical Field Theory With Two Coupled Fields

We introduce and analyze a system of two coupled partial differential equations with external noise. The equations are constructed to model transitions of monovalent metallic nanowires with non-axisymmetric intermediate or end states, but also have more general applicability. They provide a rare example of a system for which an exact solution of nonuniform stationary states can be found. We find a transition in activation behavior as the interval length on which the fields are defined is varied. We discuss several applications to physical problems.Comment: 24 page